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Search: id:A141720
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| A141720 |
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A coefficient triangle sequence of a new infinite sum polynomial set: p(x,n)=((-1 + 2*x)^(n + 1)/(-1 + x)^(n + 1))*Sum[k^n*(1 - x)^(n - k)*x^(k), {k, 0, Infinity}]; t(n,m)=Coefficients(p(x,n)). |
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+0
2
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| 1, 0, 1, 0, 1, 0, 1, 2, -2, 0, 1, 8, -8, 0, 1, 22, -6, -32, 16, 0, 1, 52, 84, -272, 136, 0, 1, 114, 606, -1168, -96, 816, -272, 0, 1, 240, 2832, -2176, -8832, 11904, -3968, 0, 1, 494, 11122, 11072, -83360, 71168, 13312, -31744, 7936, 0, 1, 1004, 39772, 148592, -472760, -17152, 831232, -707584, 176896
(list; graph; listen)
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OFFSET
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1,8
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COMMENT
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Row sums are one.
This set of polynomials comes from looking for Bernstein like polynomial
as infinite sums of the Eulerian number type.
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FORMULA
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p(x,n)=((-1 + 2*x)^(n + 1)/(-1 + x)^(n + 1))*Sum[k^n*(1 - x)^(n - k)*x^(k), {k, 0, Infinity}]; t(n,m)=Coefficients(p(x,n)).
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EXAMPLE
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{1},
{0, 1},
{0, 1},
{0, 1, 2, -2},
{0, 1, 8, -8},
{0, 1, 22, -6, -32, 16},
{0, 1, 52, 84, -272, 136},
{0, 1, 114, 606, -1168, -96, 816, -272},
{0, 1, 240, 2832, -2176, -8832, 11904, -3968},
{0, 1, 494, 11122, 11072, -83360, 71168, 13312, -31744, 7936},
{0, 1, 1004, 39772, 148592, -472760, -17152, 831232, -707584, 176896}
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MATHEMATICA
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Table[CoefficientList[FullSimplify[ExpandAll[((-1 + 2*x)^(n + 1)/(-1 +x)^(n + 1))*Sum[k^n*(1 - x)^(n - k)*x^(k), {k, 0, Infinity}]]], x], {n, 0, 10}]; Flatten[%]
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CROSSREFS
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Sequence in context: A065600 A029583 A011289 this_sequence A103272 A065710 A089799
Adjacent sequences: A141717 A141718 A141719 this_sequence A141721 A141722 A141723
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KEYWORD
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uned,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 11 2008
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